Simultaneous 1D inversion of loop–loop electromagnetic data for magnetic susceptibility and electrical conductivity

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 1857-1869 ◽  
Author(s):  
Colin G. Farquharson ◽  
Douglas W. Oldenburg ◽  
Partha S. Routh
Keyword(s):  
Magnetic Susceptibility ◽  
Objective Function ◽  
Sum Of Squares ◽  
Magnetic Data ◽  
Data Sets ◽  
Low Frequencies ◽  
Simultaneous Inversion ◽  
Electromagnetic Data ◽  
Susceptibility Effects ◽  
Logarithmic Barrier

Magnetic susceptibility affects electromagnetic (EM) loop–loop observations in ways that cannot be replicated by conductive, nonsusceptible earth models. The most distinctive effects are negative in‐phase values at low frequencies. Inverting data contaminated by susceptibility effects for conductivity alone can give misleading models: the observations strongly influenced by susceptibility will be underfit, and those less strongly influenced will be overfit to compensate, leading to artifacts in the model. Simultaneous inversion for both conductivity and susceptibility enables reliable conductivity models to be constructed and can give useful information about the distribution of susceptibility in the earth. Such information complements that obtained from the inversion of static magnetic data because EM measurements are insensitive to remanent magnetization. We present an algorithm that simultaneously inverts susceptibility‐affected data for 1D conductivity and susceptibility models. The solution is obtained by minimizing an objective function comprised of a sum‐of‐squares measure of data misfit and sum‐of‐squares measures of the amounts of structure in the conductivity and susceptibility models. Positivity of the susceptibilities is enforced by including a logarithmic barrier term in the objective function. The trade‐off parameter is automatically estimated using the generalized cross validation (GCV) criterion. This enables an appropriate fit to the observations to be achieved even if good noise estimates are not available. As well as synthetic examples, we show the results of inverting airborne data sets from Australia and Heath Steele Stratmat, New Brunswick.

scholarly journals Exploring nonlinear inversions: A 1D magnetotelluric example

2017 ◽  
Vol 36 (8) ◽  
pp. 696-699 ◽  
Author(s):  
Seogi Kang ◽  
Lindsey J. Heagy ◽  
Rowan Cockett ◽  
Douglas W. Oldenburg
Keyword(s):  
Magnetic Fields ◽  
Physical Properties ◽  
Direct Current ◽  
Magnetic Data ◽  
Data Sets ◽  
Electromagnetic Data ◽  
Problem Finding ◽  
Deconvolution Problem ◽  
Susceptibility Model ◽  
Multicomponent Data

At some point in many geophysical workflows, an inversion is a necessary step for answering the geoscientific question at hand, whether it is recovering a reflectivity series from a seismic trace in a deconvolution problem, finding a susceptibility model from magnetic data, or recovering conductivity from an electromagnetic survey. This is particularly true when working with data sets where it may not even be clear how to plot the data: 3D direct current resistivity and induced polarization surveys (it is not necessarily clear how to organize data into a pseudosection) or multicomponent data, such as electromagnetic data (we can measure three spatial components of electric and/or magnetic fields through time over a range of frequencies). Inversion is a tool for translating these data into a model we can interpret. The goal of the inversion is to find a “model” — some description of the earth's physical properties — that is consistent with both the data and geologic knowledge.

Geophysical helicopter-based magnetic methods for locating wells

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. B269-B279 ◽  
Author(s):  
Vladislav Kaminski ◽  
Richard W. Hammack ◽  
William Harbert ◽  
Garret A. Veloski ◽  
James Sams ◽  
...  
Keyword(s):  
Magnetic Susceptibility ◽  
Accurate Determination ◽  
Likelihood Estimation ◽  
Vertical Gradient ◽  
Magnetic Data ◽  
Small Subset ◽  
Data Sets ◽  
Successful Recovery ◽  
Tilt Derivative ◽  
Airborne Magnetic

We studied the problem of determining accurately the location of abandoned and sometimes undocumented wells and the challenging and increasingly important task related to subsurface reservoir integrity and regional economic development. We reviewed a variety of semiquantitative methods based on geophysical workflows, and we tested these with airborne magnetic data collected at two field sites. Our main conclusion is that airborne magnetic surveys represent a high-value tool to aid in the accurate determination of abandoned well locations and characteristics. At one site, two surveys were collected at slightly different altitudes to compare workflow robustness and allow the observed vertical magnetic gradient to be included in well detection workflows. We also investigated using focal zone anomaly statistics (using the magnetic field intensity and its first and second horizontal derivatives), analytic signal, tilt derivative, and calculated vertical gradient. In addition, we used a 3D inversion of a small subset of data to investigate the successful recovery of well-related magnetic susceptibility distribution and estimate subsurface well topology. The recovered magnetic susceptibility volume showed distinctive vertically elongated objects that correspond to known wells. Maximum likelihood estimation and confidence calculations were then applied to these data sets and indicated that high-confidence well locations could be determined and characterized using such airborne total magnetic data.

3-D inversions of magnetic gradiometer data in archeological prospecting: Possibilities and limitations

Geophysics ◽  
2000 ◽  
Vol 65 (3) ◽  
pp. 849-860 ◽  
Author(s):  
Jörg Herwanger ◽  
Hansruedi Maurer ◽  
Alan G. Green ◽  
Jürg Leckebusch
Keyword(s):  
Magnetic Susceptibility ◽  
Synthetic Data ◽  
Vertical Gradient ◽  
Magnetic Data ◽  
Data Sets ◽  
Northern Switzerland ◽  
Recorded Data ◽  
Susceptibility Contrast ◽  
Depth Extent ◽  
Archeological Site

A vertical‐gradient magnetic system based on optically pumped Cesium sensors has been used to map subtle magnetic anomalies across infilled pit houses and ditches at a medieval archeological site in northern Switzerland. For estimating the locations and dimensions of these features from the recorded data, we have designed and implemented an appropriate inversion scheme. Tests of this scheme on realistic synthetic data sets suggested that suitable minimum magnetic susceptibility contrasts and smoothing parameters for the inversion may be directly extracted from the data. Inversions with minimum magnetic susceptibility contrasts generated causative bodies with maximum plausible sizes. By using higher magnetic susceptibility contrasts, a complete suite of models that matched the data equally well was produced. To constrain better the magnetic susceptibility constrast within a selected area of the archeological site, shallow samples of topsoil and sediment were analyzed in the laboratory. An inversion based on the measured magnetic susceptibility contrast yielded reliable estimates of the locations, 3-D geometries, and sizes of two small pit houses. The depth extent of one pit house was subsequently verified by shallow drilling. We concluded that inversions of vertical‐gradient magnetic data constrained by magnetic susceptibility or shallow borehole information are rapid and inexpensive means of providing key knowledge on the depth distribution of inductively magnetized bodies.

scholarly journals Multidimensional inversion of loop-loop frequency-domain EM data for resistivity and magnetic susceptibility

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. F213-F223 ◽  
Author(s):  
Yutaka Sasaki ◽  
Jung-Ho Kim ◽  
Seong-Jun Cho
Keyword(s):  
Magnetic Susceptibility ◽  
Frequency Domain ◽  
Synthetic Data ◽  
Staggered Grid ◽  
Data Sets ◽  
Inversion Algorithm ◽  
Simultaneous Inversion ◽  
Small Loop ◽  
Em Induction ◽  
Airborne Em

Electromagnetic (EM) induction measurements are affected by resistivity and magnetic susceptibility. Thus, inverting EM data for resistivity alone can give misleading models if susceptible effects are strong. An inversion algorithm is presented to simultaneously recover multidimensional distributions of resistivity and susceptibility from various types of loop-loop frequency-domain EM data. The algorithm adopts a staggered-grid finite-difference method for the 3D forward solutions and computes the sensitivities with respect to resistivity and susceptibility from the forward solutions using the reciprocity principle. The algorithm is tested on synthetic data sets from ground-based small-loop, airborne, and Slingram EM surveys. It is shown that the simultaneous inversion of the small-loop EM data collected at a singleheight is unstable and likely to produce unreliable susceptibility models because the effect of susceptibility is nearly independent of the frequency. However, if the data are obtained for multiple heights or different loop configurations, simultaneous inversion can produce more reliable susceptibility and resistivity models even if the data are contaminated by offset errors. It is also shown that although the simultaneous inversion of airborne EM data is relatively stable, adding data obtained at different heights helps to increase the reliability of the resistivity and susceptibility models. Among the loop-loop EM methods discussed here, the Slingram method is relatively insensitive to susceptibility anomalies and thus cannot be used to recover the susceptibility distribution via inversion even if the data are obtained using different loop configurations.

Multiparameter waveform inversion of a large wide-azimuth low-frequency land data set in Oman

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. WA69-WA77 ◽  
Author(s):  
Alexandre Stopin ◽  
René-Édouard Plessix ◽  
Said Al Abri
Keyword(s):  
Waveform Inversion ◽  
Low Frequency ◽  
Large Data ◽  
Earth Model ◽  
Data Sets ◽  
Anisotropic Parameter ◽  
Data Set ◽  
Low Frequencies ◽  
Reflected Waves ◽  
Simultaneous Inversion

Several 3D seismic acoustic full-waveform inversions (FWIs) of offshore data sets have been reported over the last five years. A successful updating of the long-to-intermediate wavelengths of the earth model by FWI requires good-quality wide-angle, long-offset, low-frequency data. Recent improvements in acquisition make such data sets available on land, too. We evaluated a 3D application on a data set recorded in North Oman. The data contain low frequencies down to 1.5 Hz, long-offsets, and wide azimuths. The application of acoustic FWI on land remains complicated because of the elastic effects, notably the strong ground-roll and many acquisition and human-activity-related noises. The presence of fast carbonate layers in this region induces velocity inversions, difficult to recover from diving or postcritical waves. We accounted for anisotropic effects as we include FWI in a classical structural imaging workflow. With a dedicated processing of the data and a simultaneous inversion of the NMO velocity and the anelliptic-anisotropic parameter, we succeeded to interpret the kinematics of transmitted and reflected waves, although in the waveform inversion we included only the diving and postcritical waves. This approach has some limitations because of the acoustic assumption. We could not obtain a high-resolution image, especially at the shale-carbonate interfaces. There is also a trade-off between the NMO velocity and the anelliptic anisotropic parameter. However, the image improvements after acoustic FWI and the ability to handle the large data volume make this technique attractive in an imaging workflow.

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

Auto-weighted concept factorization for joint feature map and data representation learning

2021 ◽  
pp. 1-13
Author(s):  
Yikai Zhang ◽  
Yong Peng ◽  
Hongyu Bian ◽  
Yuan Ge ◽  
Feiwei Qin ◽  
...  
Keyword(s):  
Objective Function ◽  
Optimization Procedure ◽  
Feature Space ◽  
Representation Learning ◽  
Data Representation ◽  
Data Sets ◽  
Reconstruction Process ◽  
Factorization Model ◽  
Efficient Data ◽  
Concept Factorization

Concept factorization (CF) is an effective matrix factorization model which has been widely used in many applications. In CF, the linear combination of data points serves as the dictionary based on which CF can be performed in both the original feature space as well as the reproducible kernel Hilbert space (RKHS). The conventional CF treats each dimension of the feature vector equally during the data reconstruction process, which might violate the common sense that different features have different discriminative abilities and therefore contribute differently in pattern recognition. In this paper, we introduce an auto-weighting variable into the conventional CF objective function to adaptively learn the corresponding contributions of different features and propose a new model termed Auto-Weighted Concept Factorization (AWCF). In AWCF, on one hand, the feature importance can be quantitatively measured by the auto-weighting variable in which the features with better discriminative abilities are assigned larger weights; on the other hand, we can obtain more efficient data representation to depict its semantic information. The detailed optimization procedure to AWCF objective function is derived whose complexity and convergence are also analyzed. Experiments are conducted on both synthetic and representative benchmark data sets and the clustering results demonstrate the effectiveness of AWCF in comparison with the related models.

scholarly journals A Review of Geophysical Modeling Based on Particle Swarm Optimization

2021 ◽  
Author(s):  
Francesca Pace ◽  
Alessandro Santilano ◽  
Alberto Godio
Keyword(s):  
Particle Swarm Optimization ◽  
Inverse Modeling ◽  
Critical Evaluation ◽  
Particle Swarm ◽  
Geophysical Data ◽  
Magnetic Data ◽  
Data Sets ◽  
Swarm Optimization ◽  
Geophysical Modeling ◽  
Original Works

AbstractThis paper reviews the application of the algorithm particle swarm optimization (PSO) to perform stochastic inverse modeling of geophysical data. The main features of PSO are summarized, and the most important contributions in several geophysical fields are analyzed. The aim is to indicate the fundamental steps of the evolution of PSO methodologies that have been adopted to model the Earth’s subsurface and then to undertake a critical evaluation of their benefits and limitations. Original works have been selected from the existing geophysical literature to illustrate successful PSO applied to the interpretation of electromagnetic (magnetotelluric and time-domain) data, gravimetric and magnetic data, self-potential, direct current and seismic data. These case studies are critically described and compared. In addition, joint optimization of multiple geophysical data sets by means of multi-objective PSO is presented to highlight the advantage of using a single solver that deploys Pareto optimality to handle different data sets without conflicting solutions. Finally, we propose best practices for the implementation of a customized algorithm from scratch to perform stochastic inverse modeling of any kind of geophysical data sets for the benefit of PSO practitioners or inexperienced researchers.

Nonlinear Optimal Design of Dynamic Mechanical Systems

1992 ◽  
Author(s):  
T. E. Potter ◽  
K. D. Willmert ◽  
M. Sathyamoorthy
Keyword(s):  
Objective Function ◽  
Optimization Problems ◽  
Iteration Process ◽  
Optimization Method ◽  
Linear Constraints ◽  
Sum Of Squares ◽  
Function Evaluation ◽  
Deformation Analysis ◽  
Nonlinear Constraints ◽  
Quadratic Constraints

Abstract Mechanism path generation problems which use link deformations to improve the design lead to optimization problems involving a nonlinear sum-of-squares objective function subjected to a set of linear and nonlinear constraints. Inclusion of the deformation analysis causes the objective function evaluation to be computationally expensive. An optimization method is presented which requires relatively few objective function evaluations. The algorithm, based on the Gauss method for unconstrained problems, is developed as an extension of the Gauss constrained technique for linear constraints and revises the Gauss nonlinearly constrained method for quadratic constraints. The derivation of the algorithm, using a Lagrange multiplier approach, is based on the Kuhn-Tucker conditions so that when the iteration process terminates, these conditions are automatically satisfied. Although the technique was developed for mechanism problems, it is applicable to any optimization problem having the form of a sum of squares objective function subjected to nonlinear constraints.

Sign in / Sign up

Export Citation Format

Share Document